The architect is changing the world's skylines from Baku to Baghdad

If she builds it, they will talk. Such is the power of Zaha Hadid, the most lauded female architect in the world, whose avant-garde designs are equal parts captivating (see her gravity-defying opera house in Guangzhou, China) and controversial (see new renderings of her 2022 World Cup stadium in Qatar, which some critics say resembles female genitalia; "ridiculous," counters Hadid). The Iraqi-born architect, a member of the 2010 TIME 100, says she sees herself as part of a project to "rethink the city" one building at a time. Whereas other architects may try to mimic surrounding structures, Hadid--now helming a staff...